The 19-year-old is hot property in his homeland and made three appearances for his country at the World Cup in Russia.
Currently plying his trade with Manchester City's sister club Melbourne City, Arzani has recently been linked with a move to the Etihad, something which Rodgers all-but confirmed following his side's 3-1 win over Livingston on Saturday.
"He is, I believe, finalising his deal with Manchester City and in talks with ourselves to come in, as a possibility," Rodgers revealed. "He is another exciting young talent and we will see if we can get that organised in the next few days.
"It is not going to be (before) midweek. He has just flown in, he hasn't trained. He has obviously been at the World Cup so he will need to be in for a couple of weeks before he gets up to speed."
A loan move to the Scottish giants would seem like the perfect option for the Iran-born starlet, with Rodgers possessing a reputation for developing young talent and Celtic providing a platform for regular football.